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- Title
Infinitely many solutions for quasilinear equations with critical exponent and Hardy potential in R<sup>N</sup>
- Authors
Gao, Fengshuang; Guo, Yuxia
- Abstract
In this paper, we consider the following critical quasilinear equation with Hardy potential:{−∑Ni,j = 1 Dj(aij(u)Diu) + 1/2∑Ni,j = 1a′ij(u)DiuDju + a(x)u = ν|u|q−2u + μu/|x|2 + |u|2∗−2u,in RN, u(x) → 0 as |x| → ∞, where aij(u)∈C1(R,R), ν > 0, 0 ≤ μ < αμ, and max{αμγ/αμ−μ + 2,2∗ − 2/N−2 √μ − μ/α} (1) < q < 2∗, α,γ >0, μ = (N−2)2/4, 2∗ = 2N/N−2 is the Sobolev critical exponent. And a(x)a(x) is a finite, positive potential function satisfying suitable decay assumptions. By using truncation method combining with the regularization approximation approach and compactness arguments, we prove the existence of infinitely many solutions for this equation.
- Subjects
CRITICAL exponents; EQUATIONS; POTENTIAL functions; MATHEMATICAL regularization
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2020, Vol 40, Issue 9, p5591
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2020239